Some of the most important cryptographic characteristics of the Boolean and vector Boolean functions (nonlinearity, autocorrelation, differential uniformity) are connected with the Walsh spectrum. In this paper, we present several algorithms for computing the Walsh spectrum implemented in CUDA for parallel execution on GPU. They are based on the most popular sequential algorithm. The algorithms differ in the complexity of implementations, resources used, optimization strategies and techniques. In the end, we give some experimental results.

No abstract

In this paper, we present a library with sequential and parallel functions for computing some of the most important cryptographic characteristics of Boolean and vectorial Boolean functions. The library implements algorithms to calculate the nonlinearity, algebraic degree, autocorrelation, differential uniformity and related tables of vectorial Boolean functions. For the sake of completeness, we provide the mathematical basis of these algorithms. Furthermore, we compare the performance of the parallel functions from the developed software with the corresponding sequential functions and with analogous functions from the well-known SageMath and SET packages. Functions from BooLSPLG can be used to develop efficient algorithms for constructing Boolean and vectorial Boolean functions with good cryptographic properties. The parallel part of the library is implemented using a CUDA parallel programming model for recent NVIDIA GPU architectures. BooLSPLG is an open-source software library written in CUDA C/C++ with explicit documentation, test examples, and detailed input and output descriptions of all functions, both sequential and parallel, and it is available online.

In this paper we present a construction for S-boxes using quasi-cyclic codes. We obtain S-boxes with good nonlinearity.

No abstract